A delivery man travels 35 mi northwest to his first stop, 60 mi in a direction 35° west of south to his second stop. His third stop is supposed to be 100 mi west of his original position. What must his third displacement be (magnitude and direction) for him to reach his destination?
The Attempt at a Solution
I drew this inaccurate graph.
I'd rather not make an accurate graph for these kind of problems since I don't always have the resources to do so. I'm familiar with SOHCAHTOA, but I'm not sure how to use it to find the solution to this problem.
This is what someone suggested for a similar problem, but I'm having trouble understanding it.
Now, to your question:
- Displacement: 3.5km north, 5km west and 1.7km south gives a net distance of
√[(3.5 - 1.7)² + 5²] (Pythagorean theorem) = √28.24
to the direction of north-west (not exactly northwest)
- Direction: This is more trigonometric than geometric but whatever.
Let α be the angle between "East" axis and the direction of movement, we have:
tanα = y/x = (3.5 - 1.7)/5 = 0.36 => α = arctan(0.36)